The rectangle shown has a perimeter of 146 cm and the given area. Its length is 7 more than five times its width. Write and solve a system of equations to find the dimensions of the rectangle.

System of equations:

L = 5W + 7

2W + 2L = P

L = 62 cm

W = 11 cm

Step-by-step explanation:

Given the measurements and key words/phrases in the problem, we can set up two different equations that can be used to find both variables, length and width, of the rectangle.

The formula for perimeter of a rectangle is: 2W + 2L = P, where W = width and L = length. We also know that the L is '7 more than five times its width'. This can be written as: L = 5W + 7. Using this expression for the value of 'L', we can use the formula for perimeter and solve for width:

2W + 2 (5W + 7) = 146

Distribute: 2W + 10W + 14 = 146

Combine like terms: 12W + 14 = 146

Subtract 14 from both sides: 12W + 14 - 14 = 146 - 14 or 12W = 132

Divide 12 by both sides: 12W/12 = 132/12 or W = 11

Put '11' in for W in the equation for 'L': L = 5 (11) + 7 or L = 55 + 7 = 62.